A theoretical description is suggested for the process of tungsten erosion under current disruption in tokamak with lacking screening plasma layer. Experimental observations of substantial melting, formation of multiple small craters and erosion of a tungsten diaphragm in T-10 tokamak after current disruption are presented. Experimental observations were compared to estimates based on the model suggested. The results are used for forecasting erosion of the tungsten ITER diverter.